The main areas of scientific activity and theoretical investigations are: thermodynamics and kinetics of quantum crystals, ³He-⁴He solid solutions, atomic and molecular cryocrystals (among them two-dimensional cryocrystalline nano-systems on substrate) as well as quantum magnetic systems. Current topics of research interests are also theory of crystal lattice defects as well as acoustic and electromagnetic emission during plastic deformation of imperfect crystals. Low temperature anomalies (excessive heat) in the heat capacity of dilute solid ³He-⁴He mixtures with HCP structures were interpreted within polytypic model of the cryocrystal with haotic packing of the 2D crystalline planes on triangular lattice. The recent researches are devoted to solution of the He-He interaction promlem the rigorous quantum-mechanical statement.

1. Quantum Solids and Liquids

Thermodynamics of solid helium mixtures A consistent theory was developed for description of the temperature dependences of separating helium solid solutions heat capacity at arbitrary concentrations both below and above . It was shown that at the temperature behavior of the heat capacity is completely defined by correlation effects in the impurity subsystem. The theory of density fluctuation in solid 3He-4He solutions with arbitrary concentrations was built to explain the anomalous temperature dependences of pressure experimentally observed in the helium isotopic solid solutions. Low temperature excessive heat of dilute solid 3He-4He mixtures with HCP structures has been explained within the model of crystalline polytype with random packing of the 2D crystalline planes on triangular lattice without breaking the closest packing principle. The polytype model was also applied to explain the low temperature anomalous plastic behavior of solid parahydrogen and solid argon.

Kinetics of cryocrystals The evolution of the heterophase structure of a dilute solid solution 3He in 4He was studied theoretically. Relaxation processes in solid 3He-4He solutions was shown to be controlled by the mobility of the phase boundaries, whose velocity is determined by the quantum diffusion parameters for impurity 3He in the matrix of 4He. The quantum mechanical problem of inelastic phonon scattering on a quadrupole defect (ortho-H2 pair complex in the parahydrogen matrix) was solved and interpreted. The contribution of this mechanism to the low-temperature thermal conductivity was discussed.

Thermodynamics of cryocrystals with molecular impurities. A rigorous analytic theory was developed to describe temperature and concentration dependences of the excess impurity heat capacity of dilute solid solutions of diatomic molecules in a rare gas matrix. The theory is in excellent agreement with the experiment in the wide range of temperatures and concentrations.

Magnetism of 2D 3He monolayers. Within the Heisenberg model the theoretical approach was developed to describe thermodynamic and magnetic properties of the second 3He layer solid on graphite. It was proved the pure Heisenberg behavior of 2D solid He in the ferromagnetic regime. The proposed theory is in excellent agreement with the experimental data for all the temperatures.

Dynamics and thermodynamics of two-dimensional cryocrystals. Low-temperature dynamics and thermodynamics of two-dimensional monoatomic crystals with triangular lattice was investigated theoretically. The phonon spectra and low-temperature heat capacity were calculated analytically for monolayer structures both commensurate and incommensurate with the substrate. The obtained theoretical results provide an explanation for a great variety of experimental data on the spectra of lattice excitations and thermal properties of rare gas and helium monolayers on graphite and metal substrates.

The dynamical interaction of translational and rotational degrees of freedom of a diatomic homonuclear substitutional impurity placed in 2D close-packed atomic matrix on a substrate is investigated theoretically. It is shown that the translational-rotational interaction drastically changes inertial properties of the impurity as compared to a free rotator. Namely, this interaction leads to a strong modification of the kinetic energy operator as well as to renormalization of the crystal field parameters. Such effects can be manifested in the rotational spectrum and the impurity heat capacity of the system at low temperatures.

Interatomic interaction in condensed helium phases. The unusual physical properties of helium condensed phases (essentially different for both 3He and 4He isotopes) means that quantum nature of He-He bond (especially, dynamics of spin subsystem) should be taken into account to interpret the experimentally observable properties of the helium liquid and solid. The series of our recent research is devoted to solution of the corresponding problems in a rigorous quantum-mechanical statement.

2. Acoustic and electromagnetic emission during plastic deformation of solids.

Acoustic (AE) and electromagnetic (EME) emissions during plastic deformation of solids. Sound irradiation from dynamic dislocations and dislocation ensembles. Localized states of electrons on dislocations in metals. Mechanism of electromagnetic emission from plastically deformed ionic crystals. Correlation between AE and EME in deformed ionic crystals. Effect of gamma-irradiation on AE and EME in ionic crystals.

Selected publications:

Totalnumber of publications – over 120.

1. V.D.Natsik, K.A.Chishko. Sound radiation during annihilation of dislocations. Fizika Tverdogo Tela , 14, No. 12, 3126-3132 (1972).
2. V.D.Natsik, K.A.Chishko. Emission of sound from dislocations moving near the surface of a crystal. Fizika Tverdogo Tela , 20, No.2, 457-465 (1978); Soviet Physics: Solid State ,20, 264-269 (1978).
3. K.A.Chishko. Effect of a dislocation boundary on the internal stress distribution in a crystal. Fizika Tverdogo Tela , 23, 36-45 (1981); Soviet Physics: Solid State, 23, 20-25 (1981).
4. K.A.Chishko. Interaction of a rectilinear dislocations with a low-angle dislocation boundary. Fizika Tverdogo Tela ,23, 3028-3022 (1981); Soviet Physics: Solid State ,23, 1776-1768 (1981).
5. V.D.Natsik, K.A.Chishko. Acoustic emission of dislocations emerging the crystal surface. Akusticheskii Zhurnal ,26, No. 2, 421-429 (1982).
6. V.A.Slyusarev, K.A.Chishko. Electron localized states on edge dislocation in metal. Fizika Metallov i Metallovedenie ,58, No. 5, 877-883 (1984).
7. K.A.Chishko. Transient acoustic waves due to a screw dislocation which reaches the surface of an isotropic plate. Fizika Tverdogo Tela,31, No.1, 223-229 (1989); Soviet Physics: Solid State,31, 122-125 (1989).
8. K.A.Chishko. Emission of sound due to formation of a crack in an infinite elastic medium and at the surface of an elastic semi-infinite medium. Fizika Tverdogo Tela ,31, No. 3, 226-233 (1989); Soviet Physics: Solid State,31, 476-480 (1989).
9. K.A.Chishko. Plasticity and brittleness of cryocrystals of rare gases. Fizika Tverdogo Tela,31, N6, 283-286 (1989); Soviet Physics: Solid State,31, 1077-1079 (1989).
10. K.A.Chishko. Sound radiation caused by interaction between low-angle dislocation boundary and point obstacle. Akusticheskii Zhurnal,35, No.3, 533-540 (1989).
11. K.A.Chishko. Dynamical Green tensor and elastic fields of moving dislocation loops in isotropic plate. Akusticheskii Zhurnal ,35, No. 3, 527-532 (1989).
12. K.A.Chishko. About the spectrum of Rayleigh-Lamb waves in an isotropic elastic plate. Akusticheskii Zhurnal ,36 , No. 1, 153-159 (1990).
13. K.A.Chishko. Sound radiation during extension of a circular crack in an isotropic elastic medium. Akusticheskii Zhurnal ,36, No. 3, 541-547 (1990).
14. K.A.Chishko. Emission of normal shear waves by rectilinear dislocations on an isotropic plate. Fizika Tverdogo Tela ,33, 3051-3053 (1991); Soviet Physics: Solid State ,33, 1722-1723 (1991).
15. K.A.Chishko. Dislocation mechanism of the emission of sound during growth of a crack in a crystal. Fizika Tverdogo Tela ,34, 864-869 (1992); Soviet Physics: Solid State ,34, 462-465 (1992).
16. K.A.Chishko. Emission of Rayleigh waves on emergence of an edge dislocation on the surface of a plate, Fizika Tverdogo Tela ,34, 2236-2243 (1992); Soviet Physics: Solid State ,35, 1195-1199 (1992).
17. V.D.Natsik, K.A.Chishko. Formulation of basic problem of acoustic emission theory for solids with dispersion and attenuation. Akusticheskii Zhurnal,38, No. 3, 511-519 (1992).
18. K.A.Chishko. Emission of Rayleigh waves by a system of internal stresses sources in an isotropic elastic layer. Ukrainskii Fizicheskii Zhurnal ,37, No. 5, 745-753 (1992).
19. T.N. Antsygina, K.A.Chishko. Angular distribution of sound emitted by thin cracks. Fizika Tverdogo Tela ,35, 1797-1801 (1993); Physics of Solid State,35, 898-900 (1993).
20. K.A.Chishko. Acoustic emission by a screw dislocation emerging at an internal boundary in a crystal. Fizika Tverdogo Tela ,35, 2901-2907 (1993); Physics of Solid State ,35, 1423-1425 (1993).
21. K.A.Chishko. Emission of Lamb waves by system of internal stress sources in an isotropic elastic layer. Akusticheskii Zhurnal ,39, No. 1, 159-166 (1993).
22. K.A.Chishko. Acoustic emission images of cracks in solids. In: Acoustical Imaging ,Vol.21, Ed.by J.P.Jones, Plenum Press,1995, pp.649-660.
23. K.A.Chishko, O.V.Charkina. Emission of electromagnetic waves by edge dislocations moving in ionic crystals. Fizika Tverdogo Tela , 38, 2775-2786 (1996); Physics of Solid State ,38, 1521-1526 (1996).
24. K.A.Chishko, O.V.Charkina. Radiation of electromagnetic waves from edge dislocations moving in ionic crystals. Materials Sci. & Eng.,A234-236 , 361-364 (1997);
25. T.N. Antsygina, V.A.Slusarev, K.A.Chishko. Heat capacity of solid solutions of He in He . Low Temp. Phys. ,21, 453-457 (1995).
26. T.N. Antsygina, V.A.Slusarev, K.A.Chishko. Decomposition kinetics of solid solution of  helium isotopes. Physics of Solid State ,38, 1054-1062 (1996).
27. T.N.Antsygina, K.A.Chishko, V.A.Slusarev. Heat capacity of dilute solid solutions of  diatomic molecules in the matrix of inert gases. Phys.Rev.B 55, 3548-3558 (1997).
28. T.N.Antsygina, V.A.Slusarev, K.A.Chishko. Characteristic behavior of the specific heat of  exolving He-He solid solutions. Physics of Solid State,40, No.2, 355-361 (1998).
29. T.N.Antsygina, V.A.Slusarev, K.A.Chishko. Inelastic scattering of phonons by quadrupole  defects with internal degrees of freedom. Journ. Exp. and Theor. Phys. ,87, 303 (1998).
30. T.N.Antsygina, K.A.Chishko. Thermodynamics of He solid monolayers in the Heisenberg model. Physics of Solid State ,42, No.1, 100-108 (2000).
31. T.N.Antsygina, K.A.Chishko. Heat capacity and susceptibility of two-dimensional He solid within the Heisenberg model. Journ. Low Temp. Phys .,119, No. 5/6, 677-690 (2000).
32. M.I.Poltavskaya and K.A.Chishko. Thermodynamics of an atomic monolayer with diatomic  substitutional impurities. Low Temperature Physics ,26, No. 4, p.289-295 (2000).
33. M.I.Poltavskaya and K.A.Chishko. Spectrum of rotational states of a diatomic impurity in an atomic 2D cryocrystal. Low Temperature Physics,26, N 8, p.615-621, (2000).
34. T.N.Antsygina, K.A.Chishko, V.A.Slusarev. Correlation effects in the heat capacity of separating He-He solid solutions. Journ. Exp. and Theor. Phys .,119, No.1, 107-114 (2001).
35. T.N.Antsygina, M.I.Poltavskaya, and K.A.Chishko. Interaction of translational and rotational modes of a molecular impurity in two-dimensional atomic crystals. Physics of Solid State ,44, No.7, 1268-1277 (2002).
36. T.N.Antsygina, I.I.Poltavsky, M.I.Poltavskaya, and K.A.Chishko. Lattice dynamics and heat capacity of a two-dimensional monoatomic crystal on a substrate. Low Temperature Physics ,28, No.6, 442-451 (2002).
37. T.N.Antsygina, M.I.Poltavskaya, and K.A.Chishko. Translational-rotational interaction in dynamics and thermodynamics of 2D atomic crystal with molecular impurity. Low Temperature Physics ,29, No.9/10, 961-966 (2003).
38. T.N. Antsygina, I.I.Poltavsky, and K.A.Chishko. Thermodynamics of low-dimensional adsorption in grooves, on the outer surface, and in interstitials of a close-ended carbone nanotube bundle, Phys. Rev.B 74, N 20, 205429(10) (2006).
39. T.N. Antsygina, V.N.Grigor'ev, V.A.Maidanov, S.P.Rubets, E.Ya. Rudavskii, A.S.Rybalko, E.V.Syrnikov, and A.A.Penzev, Fluctuation effects at pre-separation region in solid 3 He- 4 He mixtures, J. Low Temp. Phys .,148, N5/6, 719-724 (2007).
40. T.N. Antsygina, I.I.Poltavsky, and K.A.Chishko, Exactly solved model for 4 He adsorption on carbon nanotube bundles: Quantitative thermodynamic description, J. Low Temp. Phys .,148, N5/6, 821-826 (2007).
41. V.Hadjicontis, C.Mavromatou, T.N. Antsygina, and K.A.Chishko, Mechanism of electromagnetic emission in plastically deformed ionic crystal, Phys. Rev.B 76 , N 2, 024106(15) (2007).
42. T.N. Antsygina, M.I.Poltavskaya, I.I.Poltavsky, and K.A.Chishko. Thermodynamics of low- dimensional spin-1/2 Heisenberg ferromagnets in magnetic field within Green function formalism, Phys. Rev.B 77, N 2, 024407(10) (2008).
43. T.N. Antsygina, M.I.Poltavskaya, I.I.Poltavsky, and K.A.Chishko, Square lattice hard-core bosons within the random phase approximation, Phys. Rev.B 80, N 17, 174511(9) (2009).
44. T.N. Antsygina, M.I.Poltavskaya, I.I.Poltavsky, and K.A.Chishko. Excitation spectra of hard-core bosons on square and triangular lattices in the superfluid phase, Phys. Rev.B 82 , N 10, 144504(10) (2010).
45. T.N. Antsygina, A.A. Lisunov, V.A. Maidanov, V.Y. Rubanskyi, S.P.Rubets, E.Ya. Rudavskii, and K.A.Chishko, Homogeneous 3He- 4He solid solutions in the pre-separation region, Physica B: Condensed Matter,406 , 3870-3875 (2011).
46. V.Hadjicontis, C.Mavromatou, D. Mastrogiannis, T.N. Antsygina, and K.A.Chishko, Relationship between electromagnetic and acoustic emissions during plastic deformation of gamma-irradiated LiF monocrystals, J. Appl. Phys.110, N 2, 024907(9) (2011).
47.  T.N.Antsygina, I.I. Poltavsky, M.I. Poltavskaya, K.A. Chishko, Magnetization of $^3$He and ³He-⁴He layers in ferromagnetic regime: Ferromagnetic anomaly and cluster size effect, Physica B: Condensed Matter, 407, P. 3925-3933 (2012).
48. T.N.Antsygina, K.A. Chishko, Structural evolution of ferromagnetic ³He monolayers adsorbed on exfoliated graphite, ФНТ, 39, N 5,P. 560-567 (2013); Low Temp. Phys. 39, N 5, 434 (2013).
49. T.N.Antsygina, K.A. Chishko, Helium atom in an external electric field: exact diagonalization, ФНТ, 40, P.1035-1044 (2014); Low Temp. Phys. 40, 807 (2014).
50. D. Mastrogiannis, T.N. Antsygina, K.A.Chishko, V.Hadjicontis, C.Mavromatou, Relationship between electromagnetic and acoustic emissions in deformed piezoelectric media: Microcracking signals, Int. J. Solids and Structures, V.56-57, P.118-125 (2014).
51. T.N.Antsygina, M.I. Poltavskaya, K.A. Chishko, The nature of the glassy phase in ⁴Не crystals, ФНТ, 41, N8, С.743–759 (2015);Low Temp. Phys. 41, 575 (2015).
52. К.А.Чишко, Е.С. Соколова, Теплоемкость ксенона, адсорбированного в канавках наносвязок, ФНТ, 42, №2, С.116-127 (2016); Low Temp. Phys. 42, 85 (2016).
53. Т.Н. Анцыгина, К.А.Чишко, Влияние структуры ядра на электронный спектр атома гелия, ФНТ, 42, N9, С.936–942 (2016); Low Temp. Phys. 42, 734 (2016).
54. T.N. Antsygina, K.A. Chishko, I.A. Degtyaryov, I.I. Poltavsky, S.S. Sokolov, N. Studart, Plasma excitation dispersion in non-degenerate quantum wire over liquid helium, Eur.Phys.J. B, 90: 79 (2017).
55. T.N. Antsygina, M.I. Poltavskaya, K.A. Chishko, Hexagonal close-packed ⁴He as crystalline multilayered polytype: An alternative for 'supersolid' or 'glassy-like' phase, J. Low Temp. Phys., 178, No.5, pp. 468-474(2017)
56. K.A. Chishko, Thermodynamics of dilute ³He–⁴He solid solutions with hcp structure, ФНТ,44, №2, pp. 154-167 (2018); Low Temp. Phys. 44, 114 (2018).
57. K.A. Chishko, Low-energy excitations in helium-like dimer within an exact diagonalization approach, ФНТ, 44, №10, 1393-1403 (2018); Low Temp. Phys. 44, 1097 (2018).
58. K.A. Chishko, A.S. Rybalko, Microwave spectroscopy of superfluid He II, ФНТ, 45, №3, pp. 384-390 (2019); Low Temp. Phys. 45, No.3 (2019).
59. K. A. Chishko, Interatomic interaction within a 4He–4He dimer with mobile nuclei, Fizika Nizkikh Temperatur, 47, №6, pp. 547–569 (2021); Low Temp. Phys. 47, No.6 (2021).

Participation in international conferences:

• 1997 – CC1997, Wroclaw-Polanica, Poland
• 1999 – LT22, Helsinki, Finland
• 2000 – CC2000, Szklarska Poreba, Poland
• 2001 – QFS2001, Konstanz, Germany
• 2002 –CC2002, Munich-Freising, Germany
• 2004 – QFS2004, Trento, Italy
• 2006 – QFS2006, Kyoto, Japan
• 2010 – QFS2010, Grenoble, France
• 2010 – CC2010, Chernogolovka, Russia
• 2012 –CC2012, Odessa, Ukraine
• 2016 – QFS2016, Prague, Czech Republic
• 2017 – ULT2017, Heidelberg, Germany
• 2018 – QFS2018, Tokyo, Japan
• 2018 – CC2018, Wroclaw, Poland